Dividing Tenths and Hundredths
Semester 4B · Chapter 14 · Lesson 4 · MATH-4B-C14-L04
Before you begin: prerequisite check
Recall: 14.01; 4A division. Attempt these questions independently first.
Calculate 2.71 × 14, where 14 is a whole number.
Show answer and reasoning
Use (10+4) groups: 271 hundredths ×14=3794 hundredths = 37.94.
Calculate 3.49 × 25, where 25 is a whole number.
Show answer and reasoning
Use (20+5) groups: 349 hundredths ×25=8725 hundredths = 87.25.
Calculate 1.05 × 25, where 25 is a whole number.
Show answer and reasoning
Use (20+5) groups: 105 hundredths ×25=2625 hundredths = 26.25.
Key vocabulary
- factor
- number being multiplied
- product
- result of multiplication
- dividend
- quantity divided into groups
- quotient
- amount in each equal group
Understand the concept
Dividing tenths or hundredths by a whole number is equal sharing of fractional units. Six tenths shared among three people gives two tenths each, or 0.2. Twenty-four hundredths shared among six groups gives four hundredths, or 0.04. Model the fractional units as tiny equal squares or equal segments. Verify a quotient by multiplying it by the divisor. A division by a whole number can yield a smaller decimal even though the digits look familiar.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
Calculate 0.06 ÷ 3.
Share 6 hundredths equally among 3 groups: 2 hundredths each = 0.02.
Check 1: try it yourself
Calculate 0.40 ÷ 5.
Show answer and reasoning
Share 40 hundredths equally among 5 groups: 8 hundredths each = 0.08.
Worked example 2
Calculate 0.26 ÷ 2.
Share 26 hundredths equally among 2 groups: 13 hundredths each = 0.13.
Check 2: try it yourself
Calculate 0.12 ÷ 4.
Show answer and reasoning
Share 12 hundredths equally among 4 groups: 3 hundredths each = 0.03.
Worked example 3
Calculate 0.28 ÷ 4.
Share 28 hundredths equally among 4 groups: 7 hundredths each = 0.07.
Check 3: try it yourself
Calculate 0.10 ÷ 5.
Show answer and reasoning
Share 10 hundredths equally among 5 groups: 2 hundredths each = 0.02.
Guided practice
Calculate 0.24 ÷ 2.
Show answer and reasoning
Share 24 hundredths equally among 2 groups: 12 hundredths each = 0.12.
Calculate 0.70 ÷ 5.
Show answer and reasoning
Share 70 hundredths equally among 5 groups: 14 hundredths each = 0.14.
Calculate 0.72 ÷ 6.
Show answer and reasoning
Share 72 hundredths equally among 6 groups: 12 hundredths each = 0.12.
Calculate 0.39 ÷ 3.
Show answer and reasoning
Share 39 hundredths equally among 3 groups: 13 hundredths each = 0.13.
Calculate 0.90 ÷ 6.
Show answer and reasoning
Share 90 hundredths equally among 6 groups: 15 hundredths each = 0.15.
Independent practice
Calculate 0.40 ÷ 4.
Show answer and reasoning
Share 40 hundredths equally among 4 groups: 10 hundredths each = 0.10.
Calculate 0.36 ÷ 6.
Show answer and reasoning
Share 36 hundredths equally among 6 groups: 6 hundredths each = 0.06.
Calculate 0.28 ÷ 2.
Show answer and reasoning
Share 28 hundredths equally among 2 groups: 14 hundredths each = 0.14.
Calculate 0.30 ÷ 2.
Show answer and reasoning
Share 30 hundredths equally among 2 groups: 15 hundredths each = 0.15.
Calculate 0.09 ÷ 3.
Show answer and reasoning
Share 9 hundredths equally among 3 groups: 3 hundredths each = 0.03.
Calculate 0.60 ÷ 5.
Show answer and reasoning
Share 60 hundredths equally among 5 groups: 12 hundredths each = 0.12.
Calculate 0.12 ÷ 6.
Show answer and reasoning
Share 12 hundredths equally among 6 groups: 2 hundredths each = 0.02.
Calculate 0.12 ÷ 2.
Show answer and reasoning
Share 12 hundredths equally among 2 groups: 6 hundredths each = 0.06.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Calculate 0.18 ÷ 3. Explain how place value or a model can check your result.
Show answer and reasoning
Share 18 hundredths equally among 3 groups: 6 hundredths each = 0.06. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “0.84 ÷ 4 = 0.21 because decimal places can be placed anywhere.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
The result 0.21 is right, but 84 hundredths shared into 4 equal groups yields 21 hundredths. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Calculate 0.54 ÷ 6.
Show answer and reasoning
Share 54 hundredths equally among 6 groups: 9 hundredths each = 0.09.
Calculate 0.06 ÷ 2.
Show answer and reasoning
Share 6 hundredths equally among 2 groups: 3 hundredths each = 0.03.
Calculate 0.12 ÷ 3.
Show answer and reasoning
Share 12 hundredths equally among 3 groups: 4 hundredths each = 0.04.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.